TMZ broke the story ... Miss Universe owner Donald Trump gave Monnin a 24-hour ultimatum to retract her statements that pageant winners are predetermined -- but Monnin refused.

So this morning, one of Donald's lawyers tells TMZ, the Miss Universe Organization -- Miss USA's parent company -- has filed suit before a private court, and intends to go after Monnin for all she's worth.

The lawsuit was not filed in a public court because of a stipulation in Monnin's contract -- which requires any dispute to be handled through private arbitration.